Calculus Question

Question

Suppose Y= squareroot (2x+1) where x and y are functions of t.

A. If  find  when  x = 4. If dx/dt = 15, find dy/dt when x = 4.

B. If  find  when x = 4. If dx/dt = 15, find dy/dt when x = 24

Answer 1

dy/dt = dy/dx dx/dt

If y = (2x+1)^1/2, dy/dx = (2x+1) ^-1/2

A dy/dt = (2x+1) ^-1/2 dx/dt = (2*4+1) ^-1/2 15 = 1/3 * 15 = 5

B dy/dt = (2x+1) ^-1/2 dx/dt = (2*24+1) ^-1/2 15 = 1/3 * 15 = 1/7 15 = 15/7